On the Density of Coprime Tuples of the Form (n, ⌊ f 1(n)⌋, …, ⌊ f k (n)⌋), Where f 1, …, f k Are Functions from a Hardy Field

Vitaly Bergelson () and Florian Karl Richter ()
Additional contact information
Vitaly Bergelson: The Ohio State University, Department of Mathematics
Florian Karl Richter: The Ohio State University, Department of Mathematics

A chapter in Number Theory – Diophantine Problems, Uniform Distribution and Applications, 2017, pp 109-135 from Springer

Abstract: Abstract Let k ∈ ℕ $$k \in \mathbb{N}$$ and let f 1, …, f k belong to a Hardy field. We prove that under some natural conditions on the k-tuple ( f 1, …, f k ) the density of the set n ∈ ℕ : gcd ( n , ⌊ f 1 ( n ) ⌋ , … , ⌊ f k ( n ) ⌋ ) = 1 } $$\displaystyle{\big\{n \in \mathbb{N}:\gcd (n,\lfloor \,f_{1}(n)\rfloor,\ldots,\lfloor \,f_{k}(n)\rfloor ) = 1\big\}}$$ exists and equals 1 ζ ( k + 1 ) $$\frac{1} {\zeta (k+1)}$$ , where ζ is the Riemann zeta function.

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-55357-3_5

Ordering information: This item can be ordered from
http://www.springer.com/9783319553573

DOI: 10.1007/978-3-319-55357-3_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().